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Some aspects of the spline smoothing approach to non-parametric regression curve fitting (with discussion). (English) Zbl 0606.62038
The regression model \(Y_ i=g(t_ i)+\epsilon_ i\) is considered. Nonparametric estimation of the function g is discussed under the assumption that the design points satisfy \(t_ 1\leq t_ 2\leq...\leq t_ n\) and that the errors \(\epsilon_ i\) are uncorrelated with zero mean. The spline smoothing approach is described and developed. The question of providing inference regions for curves is approached via finite- dimensional Bayesian formulation. The various methods presented in the paper are illustrated by examples from different fields of application. A report of a broad discussion (43 discussants) is enclosed.
Reviewer: J.Bartoszewicz

62G05 Nonparametric estimation
62J02 General nonlinear regression
65D10 Numerical smoothing, curve fitting
65C99 Probabilistic methods, stochastic differential equations